Hi DRR,
I've been in the same position many times, where I must accommodate the paying customer. I didn't intend to come across as being condescending -- I actually figured your question was the result of a client request. No need to defend your motivations :)
That said, what you're trying to accomplish really isn't possible inside DNN, and you'll have to do something "out of the box." Like I said before, one possibility would be a landing page that had a FRAMESET with one target that played the music, and the second contained the DNN site. IIS would serve, say, Frameset.html by default. The music page would have size zero. One drawback to this approach is that you risk the music continuing to play AFTER the user has navigated away from the site (because they are still in the frameset). I haven't used a FRAMESET in ages, so I'm not completely sure of the feasibility here, but this was a common approach once-upon-a-time.
Perhaps the most direct route would be for you to just launch a popup/popunder. You could accomplish this via some specific script in your skin, in a module, or anywhere really. The music would play so long as the popup/under existed. An obvious drawback to this method is that the popup would be blocked by many browsers.
A hybrid approach might be to play the music on your homepage, with a link to launch a popup with user consent. Here, users could choose which route to go. It sounds like your requirements might not allows this, however.
Flash itself might yield some possible solutions, perhaps storing the time index and restarting at that index on each page. It would pause between pages though. I have virtually zero experience with flash, so others would have to help you here.
Ultimately, you're going to need to do some experimentation to figure out which route is best. This is definitely a "non-standard" thing, and mostly will be solved outside of DNN.
Brandon